Equations For Conic Sections

The general equation of any conic section is a second order non homogeneous equation in x and y.

Equations for conic sections. Khan academy is a 501 c 3 nonprofit organization. And from that equation we can create equations for the circle ellipse parabola and hyperbola. Circles and ellipses the equation of a circle with center at a b and radius r units is x a 2 y b 2.

When working with circle conic sections we can derive the equation of a circle by using coordinates and the distance formula. The set of all points whose coordinates satisfy a given equation or condition. So the general equation that covers all conic sections is.

If the conic is non degenerate then. X h 2 a 2 y k 2 b 2 1. Here h k 0.

If b2 4ac 0 the equation represents an ellipse. If a c and b 0 the equation represents a circle which is a special case of an ellipse. Equations of conic sections.

The equations y x 2 4 and x 2 y 2 3. Therefore the equation of the circle is x 2 y 2 r 2. When x and y are both squared and the coefficients on them are the same including the sign.

Our mission is to provide a free world class education to anyone anywhere. Conic section formulas for latus rectum in hyperbola. Depending upon the restrictions applied to the terms a b c d e f we can represent equations for different conic sections.